Calculus on moduli spaces of curves (live stream)

The purpose of this talk is to survey Gerd Faltings’s contributions to the Arakelov geometry of curves. The groundwork was laid in his paper “Calculus on arithmetic surfaces”, finished in early 1983, and published in Annals in 1984. As Faltings writes in the introduction, the results of this paper turned out to be “extremely useful” to the author in finding his proof, in May 1983, of the Mordell conjecture. We present some of the fundamental ideas from loc. cit., and then proceed to discuss recent developments related to its contents. In the last couple of years, the contours of a “Calculus on moduli spaces of curves” are starting to become visible.